Best case, it accomplishes nothing, but it costs money to establish and maintain.
Sexual predator and sex-offender registries are based on two theories. The first is that sexual predators have a high recidivism rate; they are likely to re-offend. The second is that the public have a right to know if a convicted sexual predator lives in their neighborhood. I am not entirely sure I agree with such registries (my own searches for my zipcode have shown mostly people who paid for sex with prostitutes and got caught at it, not people who are a threat to me or my family), but at least a public good can be defined.
Animal abusers are not - to the best of my knowledge - recidivists in the same way sexual predators are. We don't post databases of convicted bank robbers or domestic abusers or kidnappers, but we do for those who fight dogs or throw cats in wheelie bins? Not sure how it has been established that animal abuse is a pathological illness that will continue with or without treatment.
As well, although I certainly would not like living next door to a guy who was known to have failed to feed his dogs for too long, or left his horse outside in bad weather, or kicked a cat, or so on, I would not see him as a risk for myself or my family for him to be living next door - so in what way would he be a threat to our safety? This crazy lady kept 50 cats in her garage under unsanitary conditions and a bunch of them died; she's going to invade my home and do something awful to me or my cats?
Worst-case, we get to delve into the can of worms (pardon the pun) that is animal abuse. Whilst most of can agree that inflicting needless suffering on an animal for one's sadistic pleasure is evil and wrong and bad, many of us differ on other things commonly called animal abuse, including the ritual religious slaughter of animals for food or as sacrifice in religious rituals, and then we get into just the way commercial animals are kept and treated prior to being slaughtered as food that we buy as consumers in grocery stores. Docking the ears and tails of dogs, even breeding for specific qualities, all of these have been called animal abuse at one time or another, by various people. And as much as you and I probably don't disagree much on what is and what is not animal cruelty, I'm not terribly interested in creating a list that we agree with today - knowing that tomorrow, that list might be maintained by someone with a grudge against, say, fur, or halal meat production, or even bug zappers.
Cruel treatment of animals makes me sick and angry. I am glad that certain aspects of it are criminal. That's pretty much as far as I go with it. I don't see what possible use a registry of convicted animal rights abusers would do, other than to further punish those who had served the sentences (revenge), to give politicians something to point to with pride on election day (see how much I care about my community?) and spend more tax dollars on something that creates busy-work jobs on the community nickle.
